I have set up a records repository and have created a library for our
SOPs. I have created a Content Type called "Standard Operating
Procedures" with several site columns. I have set up the library to use
the content type and when I do so, the library's metadata list is
populated with the columns from the content type.

When I try to save a doc from Word into the library, I get the
Information Panel telling me that I must fill in the required fields. I
do so, but the metadata information does not appear in the view of the
library (even though the columns are visible). When I try to check the
document in via the website, it says I must enter the required
metadata. Re-opening the document reveals that the metadata is in fact
there, and the information bar shows that it's grabbing it from the
server.

What am I doing wrong?